Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
784 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Frattini | C22 | C22×D52 |
| Fitting | C22×C4×C52 | C22 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | #532 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87900 | C2 | semidirect |
| 2. C2×C5×#709 | C2 | semidirect |
| 3. C2×C4×C5×Dic5 | C2 | semidirect |
| 4. #11717096 | C2 | semidirect |
| 5. #11717029 | C2 | semidirect |
| 6. C4×#6038 | C2 | semidirect |
| 7. #11716983 | C2 | semidirect |
| 8. #11716982 | C2 | semidirect |
| 9. #11716979 | C2 | semidirect |
| 34. C2×C4×C52 | D4 | semidirect |
| 55. C2×#709 | D5 | semidirect |
| 64. C2×C4×Dic5 | D5 | semidirect |
| 82. C5×Dic5 | #41 | semidirect |
| 152. C2×C4×C5 | D20 | semidirect |
| 153. C2×C4×C5 | C22⋊D5 | semidirect |
| 192. C52 | #532 | semidirect |
| 226. Dic5 | #709 | semidirect |
| 277. C2×C4 | #6038 | semidirect |
| 281. C5 | #65811 | semidirect |
| 282. C5 | #66166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C2×C5×#709 | 2 |
| C2×C4×C5×Dic5 | 2 |
| #11717096 | 2 |
| #11717029 | 2 |
| C4×#6038 | 2 |
| #11716983 | 2 |
| #11716982 | 2 |
| #11716979 | 2 |
| #66166 | 5 |
| #65811 | 5 |